Subgroups — C₂×#13063347 #14583681

Order 2752.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621898	C₂	1	2	yes	maximal, complemented
2	#13063347	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621873	C₂	1	2	yes	maximal, complemented
5	C₂×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₂²⋊D₄₃	—	2	2	no	—
9	#10621898	—	2	4	no	—
10	#10621898	C₂²	1	8	yes	complemented
11	C₂×D₁₇₂	C₂²	1	2	yes	—
12	C₂×C₄×D₄₃	—	2	2	no	—
13	C₂×Dic₈₆	C₂²	1	2	yes	—
14	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂²	1	4	yes	complemented
17	Dic₁₇₂	C₂²	1	4	yes	complemented
18	D₃₄₄	C₂²	1	4	yes	complemented
19	#10621873	C₂²	1	8	yes	complemented
20	C₂³×C₄₃	D₄	1	1	yes	characteristic
21	C₂²×D₄₃	—	2	2	no	—
22	C₂×C₄×C₄₃	D₄	1	2	yes	—
23	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂²⋊D₄₃	—	2	8	no	—
27	C₂×Dic₄₃	—	2	2	no	—
28	D₁₇₂	—	2	2	no	—
29	D₁₇₂	C₂³	1	4	yes	—
30	C₄×D₄₃	—	2	8	no	—
31	Dic₈₆	—	2	2	no	—
32	Dic₈₆	C₂³	1	4	yes	—
33	C₈×C₄₃	C₂³	1	2	yes	—
34	C₈×C₄₃	C₂³	1	2	yes	—
35	C₂²×C₄₃	—	2	2	no	—
36	C₂²×C₄₃	C₂×D₄	1	2	yes	—
37	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×D₄₃	—	2	4	no	—
39	C₂×D₄₃	—	4	4	no	—
40	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
41	C₄×C₄₃	C₂×D₄	1	2	yes	—
42	C₄×C₄₃	C₂⁴	1	1	yes	characteristic
43	Dic₄₃	—	2	4	no	—
44	C₂×C₄₃	—	2	2	no	—
45	C₂×C₄₃	#135	1	2	yes	complemented
46	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
47	D₄₃	—	4	4	no	—
48	C₂×#135	—	43	1	no	maximal, Sylow
49	C₄₃	C₂×#135	1	1	yes	characteristic, complemented, Sylow
50	C₂×#41	—	43	2	no	—
51	#135	—	43	8	no	—
52	C₂×Q₁₆	—	43	1	no	—
53	C₂×SD₁₆	—	43	2	no	—
54	C₂×D₈	—	43	1	no	—
55	C₂²×C₈	D₄₃	1	1	yes	characteristic, complemented
56	#41	—	43	8	no	—
57	#41	—	86	4	no	—
58	C₂×Q₈	—	43	2	no	—
59	C₂×D₄	—	43	2	no	—
60	C₂×D₄	—	86	2	no	—
61	C₂²×C₄	—	86	2	no	—
62	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
63	Q₁₆	—	43	4	no	—
64	SD₁₆	—	43	8	no	—
65	D₈	—	43	4	no	—
66	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
67	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
68	C₂×C₈	C₂×D₄₃	1	4	yes	complemented
69	C₂³	—	86	2	no	—
70	C₂³	D₁₇₂	1	1	yes	characteristic
71	Q₈	—	43	4	no	—
72	Q₈	—	86	2	no	—
73	D₄	—	43	4	no	—
74	D₄	—	86	8	no	—
75	D₄	—	86	2	no	—
76	C₂×C₄	—	86	2	no	—
77	C₂×C₄	—	86	8	no	—
78	C₂×C₄	D₁₇₂	1	2	yes	—
79	C₂×C₄	D₁₇₂	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₄₃	1	2	yes	—
82	C₈	C₂²×D₄₃	1	2	yes	—
83	C₈	C₂²×D₄₃	1	2	yes	—
84	C₂²	—	2	2	no	—
85	C₂²	—	86	4	no	—
86	C₂²	—	172	4	no	—
87	C₂²	C₂×D₁₇₂	1	2	yes	—
88	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
89	C₄	—	86	4	no	—
90	C₄	C₂×D₁₇₂	1	2	yes	—
91	C₄	C₂×D₁₇₂	1	1	yes	characteristic
92	C₄	C₂³×D₄₃	1	1	yes	characteristic
93	C₂	—	2	2	no	—
94	C₂	—	172	4	no	—
95	C₂	#13063347	1	2	yes	direct product factor
96	C₂	C₂²×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₇₂
commutator, cosocle	C₄×C₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₃
Fitting	C₂²×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
hypercenter	C₂²×C₈	D₄₃
hypocenter	C₄₃	C₂×#135
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#10621898	C₂	semidirect
2. #13063347	C₂	direct (N × H)
3. C₂×Dic₁₇₂	C₂	semidirect
4. C₂×#10621873	C₂	semidirect
5. C₂×D₃₄₄	C₂	semidirect
6. C₂²×C₈×C₄₃	C₂	semidirect
10. #10621898	C₂²	semidirect
16. C₂×C₈×C₄₃	C₂²	semidirect
17. Dic₁₇₂	C₂²	semidirect
18. D₃₄₄	C₂²	semidirect
19. #10621873	C₂²	semidirect
45. C₂×C₄₃	#135	semidirect
49. C₄₃	C₂×#135	semidirect
55. C₂²×C₈	D₄₃	semidirect
68. C₂×C₈	C₂×D₄₃	semidirect
95. C₂	#13063347	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10621898	2
#13063347	2
C₂×Dic₁₇₂	2
C₂×#10621873	2
C₂×D₃₄₄	2
C₂²×C₈×C₄₃	2
C₂×#135	43

Subgroups — C2×#13063347 #14583681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13063347 #14583681